Suppose that visitors at a theme park spend an average of $100 on souvenirs. Assume that the money spent is normally distributed with a standard deviation of $10. 

A) What are the chances that a randomly selected visitor will spend more than $120?

b) What is the chance that a randomly selected visitor will spend between $80 and $90 (inclusive)?

C) What are the chances of spending within one standard deviation, two standard deviations, and three standard deviations, respectively?

 

A. 0.02275013

B. 0.1359051

C. 0.6826895, 0.9544997, 0.9973002

The codes used are in the explanation section.

Step-by-step explanation

Here are the codes i use to compute for the probabilities

A.  1- pnorm(120, mean=100, sd = 10) // since the problem concerns with x>120 i subtracted the prob of x=120 to 1.

B. pnorm(90, mean=100, sd = 10)- pnorm(80, mean = 100, sd =10 ) //subtract prob of x=80 to x=90 since the pnorm fuction will calculate the area under the normal curve to the left of x.

C.  

• pnorm(110, mean=100, sd = 10)- pnorm(90, mean = 100, sd =10 )
• pnorm(120, mean=100, sd = 10)- pnorm(80, mean = 100, sd =10 )
• pnorm(130, mean=100, sd = 10)- pnorm(70, mean = 100, sd =10 )

I used the pnorm function in r since this function calculates the area under the curve of a normal distribution/ probability of a normal distribution.